from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5577, base_ring=CyclotomicField(390))
M = H._module
chi = DirichletCharacter(H, M([0,78,5]))
chi.galois_orbit()
[g,chi] = znchar(Mod(4,5577))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(5577\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(390\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1859.bs | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{5577}(4,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{390}\right)\) | \(e\left(\frac{83}{195}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{301}{390}\right)\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{166}{195}\right)\) | \(e\left(\frac{131}{195}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5577}(49,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{301}{390}\right)\) | \(e\left(\frac{106}{195}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{227}{390}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{17}{195}\right)\) | \(e\left(\frac{172}{195}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5577}(82,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{371}{390}\right)\) | \(e\left(\frac{176}{195}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{307}{390}\right)\) | \(e\left(\frac{111}{130}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{157}{195}\right)\) | \(e\left(\frac{17}{195}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5577}(322,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{390}\right)\) | \(e\left(\frac{127}{195}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{329}{390}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{59}{195}\right)\) | \(e\left(\frac{184}{195}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5577}(355,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{287}{390}\right)\) | \(e\left(\frac{92}{195}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{289}{390}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{184}{195}\right)\) | \(e\left(\frac{164}{195}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5577}(394,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{390}\right)\) | \(e\left(\frac{119}{195}\right)\) | \(e\left(\frac{97}{130}\right)\) | \(e\left(\frac{253}{390}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{43}{195}\right)\) | \(e\left(\frac{68}{195}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5577}(400,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{133}{390}\right)\) | \(e\left(\frac{133}{195}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{191}{390}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{71}{195}\right)\) | \(e\left(\frac{76}{195}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5577}(433,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{263}{390}\right)\) | \(e\left(\frac{68}{195}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{61}{390}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{136}{195}\right)\) | \(e\left(\frac{11}{195}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5577}(478,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{390}\right)\) | \(e\left(\frac{61}{195}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{287}{390}\right)\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{122}{195}\right)\) | \(e\left(\frac{7}{195}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5577}(511,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{161}{390}\right)\) | \(e\left(\frac{161}{195}\right)\) | \(e\left(\frac{93}{130}\right)\) | \(e\left(\frac{67}{390}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{127}{195}\right)\) | \(e\left(\frac{92}{195}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5577}(751,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{277}{390}\right)\) | \(e\left(\frac{82}{195}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{389}{390}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{164}{195}\right)\) | \(e\left(\frac{19}{195}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5577}(784,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{390}\right)\) | \(e\left(\frac{77}{195}\right)\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{49}{390}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{154}{195}\right)\) | \(e\left(\frac{44}{195}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5577}(790,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{319}{390}\right)\) | \(e\left(\frac{124}{195}\right)\) | \(e\left(\frac{47}{130}\right)\) | \(e\left(\frac{203}{390}\right)\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{53}{195}\right)\) | \(e\left(\frac{43}{195}\right)\) | \(e\left(\frac{29}{30}\right)\) |
| \(\chi_{5577}(829,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{283}{390}\right)\) | \(e\left(\frac{88}{195}\right)\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{251}{390}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{176}{195}\right)\) | \(e\left(\frac{106}{195}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5577}(862,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{390}\right)\) | \(e\left(\frac{53}{195}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{211}{390}\right)\) | \(e\left(\frac{53}{130}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{106}{195}\right)\) | \(e\left(\frac{86}{195}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5577}(907,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{211}{390}\right)\) | \(e\left(\frac{16}{195}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{347}{390}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{32}{195}\right)\) | \(e\left(\frac{37}{195}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5577}(940,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{341}{390}\right)\) | \(e\left(\frac{146}{195}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{217}{390}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{97}{195}\right)\) | \(e\left(\frac{167}{195}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5577}(1180,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{390}\right)\) | \(e\left(\frac{37}{195}\right)\) | \(e\left(\frac{111}{130}\right)\) | \(e\left(\frac{59}{390}\right)\) | \(e\left(\frac{37}{130}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{74}{195}\right)\) | \(e\left(\frac{49}{195}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5577}(1213,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{257}{390}\right)\) | \(e\left(\frac{62}{195}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{199}{390}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{124}{195}\right)\) | \(e\left(\frac{119}{195}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5577}(1219,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{390}\right)\) | \(e\left(\frac{79}{195}\right)\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{263}{390}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{158}{195}\right)\) | \(e\left(\frac{73}{195}\right)\) | \(e\left(\frac{29}{30}\right)\) |
| \(\chi_{5577}(1252,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{390}\right)\) | \(e\left(\frac{89}{195}\right)\) | \(e\left(\frac{7}{130}\right)\) | \(e\left(\frac{163}{390}\right)\) | \(e\left(\frac{89}{130}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{23}{195}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5577}(1258,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{390}\right)\) | \(e\left(\frac{43}{195}\right)\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{311}{390}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{86}{195}\right)\) | \(e\left(\frac{136}{195}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5577}(1291,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{233}{390}\right)\) | \(e\left(\frac{38}{195}\right)\) | \(e\left(\frac{49}{130}\right)\) | \(e\left(\frac{361}{390}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{76}{195}\right)\) | \(e\left(\frac{161}{195}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{5577}(1336,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{361}{390}\right)\) | \(e\left(\frac{166}{195}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{17}{390}\right)\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{137}{195}\right)\) | \(e\left(\frac{67}{195}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{5577}(1369,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{390}\right)\) | \(e\left(\frac{131}{195}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{367}{390}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{67}{195}\right)\) | \(e\left(\frac{47}{195}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{5577}(1609,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{390}\right)\) | \(e\left(\frac{187}{195}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{119}{390}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{179}{195}\right)\) | \(e\left(\frac{79}{195}\right)\) | \(e\left(\frac{17}{30}\right)\) |
| \(\chi_{5577}(1642,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{390}\right)\) | \(e\left(\frac{47}{195}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{349}{390}\right)\) | \(e\left(\frac{47}{130}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{94}{195}\right)\) | \(e\left(\frac{194}{195}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{5577}(1648,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{229}{390}\right)\) | \(e\left(\frac{34}{195}\right)\) | \(e\left(\frac{37}{130}\right)\) | \(e\left(\frac{323}{390}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{68}{195}\right)\) | \(e\left(\frac{103}{195}\right)\) | \(e\left(\frac{29}{30}\right)\) |
| \(\chi_{5577}(1681,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{269}{390}\right)\) | \(e\left(\frac{74}{195}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{313}{390}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{148}{195}\right)\) | \(e\left(\frac{98}{195}\right)\) | \(e\left(\frac{19}{30}\right)\) |
| \(\chi_{5577}(1687,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{390}\right)\) | \(e\left(\frac{193}{195}\right)\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{371}{390}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{191}{195}\right)\) | \(e\left(\frac{166}{195}\right)\) | \(e\left(\frac{23}{30}\right)\) |
| \(\chi_{5577}(1720,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{390}\right)\) | \(e\left(\frac{23}{195}\right)\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{121}{390}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{46}{195}\right)\) | \(e\left(\frac{41}{195}\right)\) | \(e\left(\frac{13}{30}\right)\) |